This is my in-expert opinion.
I'm not sure that "natural fragrance" has an official, legal definition. Much like "natural" doesn't have an official, legal definition. You could call a detergent bar artificially scented and colored with Red Dye #40 "natural" if you wanted to.
That being said, I think that essential oils (EOs) are probably the #1 natural fragrance. Some others might be extracts and absolutes. For example, you can't get rose or jasmine essential oil, because to get the fragrance from the plants, you have to use solvents. So some would argue that absolutes aren't natural b/c of that.
If you are making soap (CP or HP) your options for natural fragrances are limited b/c the lye monster will gobble up a lot of things. For example, vanilla extract isn't going to stand up to the raw soap (and the alcohol in it will cause the soap to separate), but it might work in a lotion or in some kind of body spray.
Phthlate free doesn't equal natural.
You can also check out floral waxes (Camden Grey carries some). I made a solid perfume using Rose floral wax that I really like. If you are making a product with water (lotion, etc), you could experiment with hydrosols (I know Majestic Mountain Sage carries a good variety). Also, you can find rose water and orange blossom water at some health food stores and ethnic food stores.
Our general definition is that a body butter doesn't contain water but is all oils, butters, waxes, etc. Vs say a thick lotion or cream, that does contain water. Just letting you know to help you "speak our language" a bit better, as you skim through the forum.
It might help us for you to get more specific. what type of product(s) do you want to make, and what scents do you want to use?